On stabilized space‐time FEM for anisotropic meshes: Incompressible Navier–Stokes equations and applications to blood flow in medical devices

In complex applications, such as the analysis of hydraulic performance of blood pumps (ventricular assist devices), the Navier–Stokes equations have to be discretized on very anisotropic meshes. If stabilized finite element formulations are applied, standard definitions of the stabilization parameter are usually not appropriate to handle elements with a high aspect ratio. If, in addition, rotating objects, moving meshes, or turbulence has to be considered in the simulation, further modifications of the stabilization procedure have to be applied. In this paper, we present stabilized space‐time finite element formulations of the incompressible Navier–Stokes equations that show very good convergence properties on complex anisotropic meshes and lead to reasonable numerical accuracy in complex flows when compared with experimental data. Copyright © 2017 John Wiley & Sons, Ltd.     

A frame invariant and maximum principle enforcing second‐order extension for cell‐centered ALE schemes based on local convex hull preservation

Two difficulties are clearly identified for high‐order extensions of ALE schemes for Euler equations: strict respect of the maximum principle and preservation of the Galilean invariance. We deal with these two issues in this paper. Our approach is closely related to the concepts of a posteriori limiting and convex hull spanning. We introduce the notion of local convex hull preservation schemes, which embodies these two concepts. We lean on this notion to propose a fully Galilean invariant ALE scheme. Moreover, we provide a new limiter (called Apitali for A Posteriori ITerAtive LImiter) for the remap step, enforcing the local convex hull preservation property. Copyright © 2014 John Wiley & Sons, Ltd.     

流体-结构耦合问题的有限元并行计算研究

流体-结构耦合问题广泛存在于各种工程领域,本文采用ALE显式有限元法求解该类问题,并对该方法的并行性进行讨论。同时根据流体-结构耦合问题与ALE显式有限元的计算特点,在坐标递归分区方法的基础上设计并程序实现了基于流体-结构耦合均衡的分区算法。通过与坐标递归分区方法的计算结果相比较,对于流体-结构耦合问题的求解,耦合均衡并行分区方法具有更好的加速比和并行效率。     

The Plane Wedge Problem Loaded at Its Apex – the Self-similarity Property and the Characteristic Vector

In the present paper the elastostatic problem of a generally anisotropic and angularly inhomogeneous plane wedge loaded at its apex by a concentrated force, is studied in linear elasticity. At first the self-similarity property is formulated and the stress field of the inhomogeneous anisotropic self-similar wedge problem, is deduced. The wedge is radially separated and the plane wedge problem is reformulated by the introduction of a characteristic vector. Furthermore, the angular distribution of the load is determined. The multi-material wedge problem in terms of a formulation based on the isotropic angularly inhomogeneous wedge, is confronted, and necessary conditions that ensure the self-similarity property, are found. Finally, the similar elastostatic wedge problems and the involution between stresses, are studied. Mathematics Subject Classifications (2000) 74B05, 74K30, 34B05, 51N15.     

带环形隔板的圆柱储箱内液体晃动阻尼分析

根据现有的阻尼理论，在线性势流的假设下，分别对带刚性和弹性隔板的圆柱形储液箱内液体晃动做了 有限元仿真计算. 计算结果与实验测定结果相比较发现，在晃动频率上符合得很好，但阻尼 比相差较大. 同时, 通过ALE有限元数值仿真，对储箱内无隔板和有隔板情况下的 黏性流体晃动做了比较，初步推定隔板对液体晃动的``滞阻'的一个重要表现形式为涡耗散.     

Modeling spherical explosions with aluminized energetic materials

This paper deals with the numerical solution and validation of a reactive flow model dedicated to the study of spherical explosions with an aluminized energetic material. Situations related to air blast as well as underwater explosions are examined. Such situations involve multiscale phenomena associated with the detonation reaction zone, the aluminium reaction zone, the shock propagation distance and the bubble oscillation period. A detonation tracking method is developed in order to avoid the detonation structure computation. An ALE formulation is combined to the detonation tracking method in order to solve the material interface between detonation products and the environment as well as shock propagation. The model and the algorithm are then validated over a wide range of spherical explosions involving several types of explosives, both in air and liquid water environment. Large-scale experiments have been done in order to determine the blast wave effects with explosive compositions of variable aluminium content. In all situations the agreement between computed and experimental results is very good.     

A COMPARATIVE STUDY OF THE OPENING AND CLOSING PROCESS OF TWO TYPES OF MECHANICAL HEART VALVES USING ALE FINITE ELEMENT METHOD

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Numerical study of a thin liquid film flowing down an inclined wavy plane

We investigate the stability of a thin liquid film flowing down an inclined wavy plane using a direct numerical solver based on a finite element/arbitrary Lagrangian Eulerian approximation of the free-surface Navier-Stokes equations. We study the dependence of the critical Reynolds number for the onset of surface wave instabilities on the inclination angle, the waviness parameter, and the wavelength parameter, focusing in particular on mild inclinations and relatively large waviness so that the bottom does not fall monotonously. In the present parameter range, shorter wavelengths and higher amplitude for the bottom undulation stabilize the flow. The dependence of the critical Reynolds number evaluated with the Nusselt flow rate on the inclination angle is more complex than the classical relation (5/6 times the cotangent of the inclination angle), but this dependence can be recovered if the actual flow rate at critical conditions is used instead.     

The error‐minimization‐based rezone strategy for arbitrary Lagrangian‐Eulerian methods

The objective of the Arbitrary Lagrangian‐Eulerian (ALE) methodology for solving multidimensional fluid flow problems is to move the computational mesh, using the flow as a guide, to improve the robustness, accuracy and efficiency of a simulation. The main elements in the ALE simulation are an explicit Lagrangian phase, a rezone phase in which a new mesh is defined, and a remapping (conservative interpolation) phase, in which the Lagrangian solution is transferred to the new mesh. In most ALE codes, the main goal of the rezone phase is to maintain high quality of the rezoned mesh. In this article, we describe a new rezone strategy which minimizes the L₂ norm of the solution error and maintains smoothness of the mesh. The efficiency of the new method is demonstrated with numerical experiments. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh

^{The aim of this paper is to investigate the stability and convergenceof time integration schemes for the solution of a semi-discretizationof a model parabolic problem in 1D using a moving mesh. Thespatial discretization is achieved using a second-order centralfinite-difference scheme. Using energy techniques we show thatthe backward Euler scheme is unconditionally stable in a mesh-dependentL₂-norm, independently of the mesh movement, but the Crank–Nicolson(CN) scheme is only conditionally stable. By identifying thediffusive and anti-diffusive effects caused by the mesh movement,we devise an adaptive -method that is shown to be unconditionallystable and asymptotically second-order accurate. Numerical experimentsare presented to back up the findings of the analysis.}